In this paper,the Paley-Wiener theorem is extended to the analytic function spaces with general weights.We first generalize the theorem to weighted Hardy spaces Hp(0<p<∞)on tube domains by constructing a sequen...In this paper,the Paley-Wiener theorem is extended to the analytic function spaces with general weights.We first generalize the theorem to weighted Hardy spaces Hp(0<p<∞)on tube domains by constructing a sequence of L^(1)functions converging to the given function and verifying their representation in the form of Fourier transform to establish the desired result of the given function.Applying this main result,we further generalize the Paley-Wiener theorem for band-limited functions to the analytic function spaces L^(p)(0<p<∞)with general weights.展开更多
High pressure and water-bearing caverns ahead of a karst tunnel face tend to cause geological disasters, such as water and mud bursts. So, the determination of safe thickness of the reserved rock plug is a key technic...High pressure and water-bearing caverns ahead of a karst tunnel face tend to cause geological disasters, such as water and mud bursts. So, the determination of safe thickness of the reserved rock plug is a key technical problem to be solved for karst tunnel construction. Based on the Hoek-Brown nonlinear failure criterion, the minimum safe thickness of rock plug was investigated in the light of the limit analysis theory. On the basis of the proposed failure mode, the expression of the minimum thickness for rock plug was obtained by means of upper bound theorem in combination with variational principle. The calculation results show the influence of each parameter on safe thickness and reveal the damage range of rock plug. The proposed method is verified by comparing the results with those of the drain cavern of Maluqing Tunnel. The research shows that with the increase of compressive strength and tensile strength as well as constant A of Hoek-Brown criterion, the safe thickness decreases, whereas with the increase of cavern pressure, tunnel diameter, and constant B from Hoek-Brown criterion, the safe thickness increases. Besides, the tensile strength, or constants A and B affect the shear failure angle of rock plug structure, but other parameters do not. In conclusion, the proposed method can predict the minimum safe thickness of rock plug, and is useful for water burst study and prevention measures of tunnels constructed in high-risk karst regions.展开更多
Based on the characteristic that the potential sliding surfaces of rock slope are commonly in the shape of either line or fold line,analysis thought of conventional pile foundation in the flat ground under complex loa...Based on the characteristic that the potential sliding surfaces of rock slope are commonly in the shape of either line or fold line,analysis thought of conventional pile foundation in the flat ground under complex load condition was applied and the upper-bound theorem of limit analysis was used to compute thrust of rock layers with all possible distribution shapes. The interaction of slope and pile was considered design load in terms of slope thrust,and the finite difference method was derived to calculate inner-force and displacement of bridge pile foundation in rock slope under complex load condition. The result of example shows that the distribution model of slope thrust has certain impact on displacement and inner-force of bridge pile foundation. The maximum displacement growth rate reaches 54% and the maximum moment and shear growth rates reach only 15% and 20%,respectively,but the trends of inner-force and displacement of bridge pile foundation are basically the same as those of the conventional pile foundation in the flat ground. When the piles bear the same level lateral thrust,the distribution shapes of slope thrust have different influence on inner-force of pile foundation,especially the rectangle distribution,and the triangle thrust has the smallest displacement and inner-force of pile foundation.展开更多
By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established...By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.展开更多
We present a method for using type theory to solve decision making problem. Our method is based on the view that decision making is a special kind of theorem proving activity. An isomorphism between problems and types...We present a method for using type theory to solve decision making problem. Our method is based on the view that decision making is a special kind of theorem proving activity. An isomorphism between problems and types, and solutions and programs has been established to support this view which is much similar to the Curry-Howard isomorphism between propositions and types, and proofs and programs. To support our method, a proof development system called PowerEpsilon has been developed, and the synthesis of a decision procedure for validity of first-order propositional logic is discussed to show the power of the system.展开更多
In this paper, the global controllability for a class of high dimensional polynomial systems has been investigated and a constructive algebraic criterion algorithm for their global controllability has been obtained. B...In this paper, the global controllability for a class of high dimensional polynomial systems has been investigated and a constructive algebraic criterion algorithm for their global controllability has been obtained. By the criterion algorithm, the global controllability can be determined in finite steps of arithmetic operations. The algorithm is imposed on the coefficients of the polynomials only and the analysis technique is based on Sturm Theorem in real algebraic geometry and its modern progress. Finally, the authors will give some examples to show the application of our results.展开更多
This paper takes further insight into the sparse geometry which offers a larger array aperture than uniform linear array(ULA)with the same number of physical sensors.An efficient method based on closed-form robust Chi...This paper takes further insight into the sparse geometry which offers a larger array aperture than uniform linear array(ULA)with the same number of physical sensors.An efficient method based on closed-form robust Chinese remainder theorem(CFRCRT)is presented to estimate the direction of arrival(DOA)from their wrapped phase with permissible errors.The proposed algorithm has significantly less computational complexity than the searching method while maintaining similar estimation precision.Furthermore,we combine all phase discrete Fourier transfer(APDFT)and the CFRCRT algorithm to achieve a considerably high DOA estimation precision.Both the theoretical analysis and simulation results demonstrate that the proposed algorithm has a higher estimation precision as well as lower computation complexity.展开更多
In this paper,we consider a Schr¨odinger-Poisson system with sublinear nonlinearity.The growth of nonlinearity depends on potential function and a bounded function.We first obtain the existence of nontrivial solu...In this paper,we consider a Schr¨odinger-Poisson system with sublinear nonlinearity.The growth of nonlinearity depends on potential function and a bounded function.We first obtain the existence of nontrivial solution sequence with negative energy for the system via a variant Clark’s theorem.Then we get the asymptotical property of the solution sequence by L∞norm.展开更多
This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic diff...This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic differential equations.Then we obtain a comparison theorem in one-dimensional situation.展开更多
针对覆冰输电导线舞动问题,基于概率密度演化法,提出了一种覆冰输电导线起舞概率分析方法。首先,建立了基于临界风速的覆冰输电导线起舞功能函数,结合具有3个平动自由度与1个扭转自由度的三结点索单元的有限元模型与李雅普诺夫稳定性定...针对覆冰输电导线舞动问题,基于概率密度演化法,提出了一种覆冰输电导线起舞概率分析方法。首先,建立了基于临界风速的覆冰输电导线起舞功能函数,结合具有3个平动自由度与1个扭转自由度的三结点索单元的有限元模型与李雅普诺夫稳定性定理,求解了覆冰输电导线起舞临界风速;其次,基于概率密度演化法,发展了一种覆冰输电导线起舞概率评估框架,并进行覆冰输电导线起舞概率的计算与分析;最后,获得了某单跨覆冰导线算例的起舞概率并进行了参数分析。分析结果表明:本研究方法可准确计算该单跨输电导线的起舞概率,在计算效率上相比拉丁超立方抽样-蒙特卡洛模拟法(Latin hypercube sampling-Monte Carlo simulation,简称LHS-MCS)具有显著优势;档距、初始水平张力与初始风攻角对该单跨输电导线的起舞概率影响较大。展开更多
基金Supported by the National Natural Science Foundation of China(12301101)the Guangdong Basic and Applied Basic Research Foundation(2022A1515110019 and 2020A1515110585)。
文摘In this paper,the Paley-Wiener theorem is extended to the analytic function spaces with general weights.We first generalize the theorem to weighted Hardy spaces Hp(0<p<∞)on tube domains by constructing a sequence of L^(1)functions converging to the given function and verifying their representation in the form of Fourier transform to establish the desired result of the given function.Applying this main result,we further generalize the Paley-Wiener theorem for band-limited functions to the analytic function spaces L^(p)(0<p<∞)with general weights.
基金Project(2013CB036004)supported by the National Basic Research Program of ChinaProject(51378510)supported by the National Natural Science Foundation of ChinaProject(CX2014B069)supported by Hunan Provincial Innovation Foundation for Postgraduate,China
文摘High pressure and water-bearing caverns ahead of a karst tunnel face tend to cause geological disasters, such as water and mud bursts. So, the determination of safe thickness of the reserved rock plug is a key technical problem to be solved for karst tunnel construction. Based on the Hoek-Brown nonlinear failure criterion, the minimum safe thickness of rock plug was investigated in the light of the limit analysis theory. On the basis of the proposed failure mode, the expression of the minimum thickness for rock plug was obtained by means of upper bound theorem in combination with variational principle. The calculation results show the influence of each parameter on safe thickness and reveal the damage range of rock plug. The proposed method is verified by comparing the results with those of the drain cavern of Maluqing Tunnel. The research shows that with the increase of compressive strength and tensile strength as well as constant A of Hoek-Brown criterion, the safe thickness decreases, whereas with the increase of cavern pressure, tunnel diameter, and constant B from Hoek-Brown criterion, the safe thickness increases. Besides, the tensile strength, or constants A and B affect the shear failure angle of rock plug structure, but other parameters do not. In conclusion, the proposed method can predict the minimum safe thickness of rock plug, and is useful for water burst study and prevention measures of tunnels constructed in high-risk karst regions.
基金Project(50578060) supported by the National Natural Science Foundation of China
文摘Based on the characteristic that the potential sliding surfaces of rock slope are commonly in the shape of either line or fold line,analysis thought of conventional pile foundation in the flat ground under complex load condition was applied and the upper-bound theorem of limit analysis was used to compute thrust of rock layers with all possible distribution shapes. The interaction of slope and pile was considered design load in terms of slope thrust,and the finite difference method was derived to calculate inner-force and displacement of bridge pile foundation in rock slope under complex load condition. The result of example shows that the distribution model of slope thrust has certain impact on displacement and inner-force of bridge pile foundation. The maximum displacement growth rate reaches 54% and the maximum moment and shear growth rates reach only 15% and 20%,respectively,but the trends of inner-force and displacement of bridge pile foundation are basically the same as those of the conventional pile foundation in the flat ground. When the piles bear the same level lateral thrust,the distribution shapes of slope thrust have different influence on inner-force of pile foundation,especially the rectangle distribution,and the triangle thrust has the smallest displacement and inner-force of pile foundation.
文摘By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.
文摘We present a method for using type theory to solve decision making problem. Our method is based on the view that decision making is a special kind of theorem proving activity. An isomorphism between problems and types, and solutions and programs has been established to support this view which is much similar to the Curry-Howard isomorphism between propositions and types, and proofs and programs. To support our method, a proof development system called PowerEpsilon has been developed, and the synthesis of a decision procedure for validity of first-order propositional logic is discussed to show the power of the system.
基金supported by the Natural Science Foundation of China under Grant Nos.60804008,61174048and 11071263the Fundamental Research Funds for the Central Universities and Guangdong Province Key Laboratory of Computational Science at Sun Yat-Sen University
文摘In this paper, the global controllability for a class of high dimensional polynomial systems has been investigated and a constructive algebraic criterion algorithm for their global controllability has been obtained. By the criterion algorithm, the global controllability can be determined in finite steps of arithmetic operations. The algorithm is imposed on the coefficients of the polynomials only and the analysis technique is based on Sturm Theorem in real algebraic geometry and its modern progress. Finally, the authors will give some examples to show the application of our results.
基金supported by the Fund for Foreign Scholars in University Research and Teaching Programs(the 111 Project)(B18039)
文摘This paper takes further insight into the sparse geometry which offers a larger array aperture than uniform linear array(ULA)with the same number of physical sensors.An efficient method based on closed-form robust Chinese remainder theorem(CFRCRT)is presented to estimate the direction of arrival(DOA)from their wrapped phase with permissible errors.The proposed algorithm has significantly less computational complexity than the searching method while maintaining similar estimation precision.Furthermore,we combine all phase discrete Fourier transfer(APDFT)and the CFRCRT algorithm to achieve a considerably high DOA estimation precision.Both the theoretical analysis and simulation results demonstrate that the proposed algorithm has a higher estimation precision as well as lower computation complexity.
基金Supported by National Natural Science Foundation of China （60872046） the Key Discipline Development Program of Beijing Municipal Commission （XK100080537）
基金Supported by the National Natural Science Foundation of China(12226412)Natural Science Foundation of Jiangsu Province(BK20221339)。
文摘In this paper,we consider a Schr¨odinger-Poisson system with sublinear nonlinearity.The growth of nonlinearity depends on potential function and a bounded function.We first obtain the existence of nontrivial solution sequence with negative energy for the system via a variant Clark’s theorem.Then we get the asymptotical property of the solution sequence by L∞norm.
基金Supported by the National Natural Science Foundation of China(12001074)the Research Innovation Program of Graduate Students in Hunan Province(CX20220258)+1 种基金the Research Innovation Program of Graduate Students of Central South University(1053320214147)the Key Scientific Research Project of Higher Education Institutions in Henan Province(25B110025)。
文摘This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic differential equations.Then we obtain a comparison theorem in one-dimensional situation.
文摘针对覆冰输电导线舞动问题,基于概率密度演化法,提出了一种覆冰输电导线起舞概率分析方法。首先,建立了基于临界风速的覆冰输电导线起舞功能函数,结合具有3个平动自由度与1个扭转自由度的三结点索单元的有限元模型与李雅普诺夫稳定性定理,求解了覆冰输电导线起舞临界风速;其次,基于概率密度演化法,发展了一种覆冰输电导线起舞概率评估框架,并进行覆冰输电导线起舞概率的计算与分析;最后,获得了某单跨覆冰导线算例的起舞概率并进行了参数分析。分析结果表明:本研究方法可准确计算该单跨输电导线的起舞概率,在计算效率上相比拉丁超立方抽样-蒙特卡洛模拟法(Latin hypercube sampling-Monte Carlo simulation,简称LHS-MCS)具有显著优势;档距、初始水平张力与初始风攻角对该单跨输电导线的起舞概率影响较大。
